Minimizing Total Completion Time Subject to Job Release Dates and Preemption Penalties

Extensive research has been devoted to preemptive scheduling. However, little attention has been paid to problems where a certain time penalty must be incurred if preemption is allowed. In this paper, we consider the single-machine scheduling problem of minimizing the total completion time subject to job release dates and preemption penalties, where each time a job is started, whether initially or after being preempted, a job-independent setup must take place. The problem is proved to be strongly NP-hard even if the setup time is one unit. We also study a natural extension of a greedy algorithm, which is optimal in the absence of preemption penalty. It is proved that the algorithm has a worst-case performance bound of 25/16, even when the maximum completion time, i.e., makespan, criterion is considered simultaneously.     

A two-phase approach to solve the synchronized bin–forklift scheduling problem

In this paper, we propose a two-phase approach to solve a combined routing and scheduling problem that occurs in the textile industry: fabrics are dyed by dye-jets and transported by forklifts. The objective is to minimize the cost of the unproductive activities, i.e., the dye-jet setup times and the forklift waiting time. The first phase solves an integer linear program to assign jobs (fabrics) to dye-jets while minimizing the setup cost; we compare an arc-based and a path-based formulation. The second phase uses a mixed-integer linear program for the dye-jet scheduling and both the routing and scheduling of forklifts. Experiments are performed on real data provided by a major multinational company, and larger test problems are randomly generated to assess the algorithm. The tests were conducted using Cplex 12.6.0 and a column generation solver. The numerical results show that our approach is efficient in terms of both solution quality and computational time.     

A single machine carryover sequence-dependent group scheduling in PCB manufacturing

This paper considers the problem of minimizing the makespan on a single machine with carryover sequence-dependent setup times. A similar problem with multi-machine flow shop usually arises in the assembly of printed circuit boards (PCBs). This research investigates the possibility of processing all components of PCBs using just one machine. By doing so the operational costs of having multi-machines can be reduced, and as a result, finding an optimal solution might be more plausible. The objective is to minimize the maximum completion time of all board groups, commonly known as makespan. The operational constraints are such that all board types within a board group must be completely kitted, as it is traditionally performed by kitting staff, before that board group begins its assembly operation. We introduce the external setup (kitting) time and require that it be performed solely by the machine operator during the run time of the current board group, and thereby completely eliminating the need for kitting staff. The carryover sequence-dependent setup time, namely the internal (machine) setup time, is realized when a new board group is ready for assembly operation and is dependent on all of the previously scheduled board groups and their sequences. To the best of our knowledge, this is the first time the external and internal setup times are integrated in PCB group scheduling research. We develop a branch-and-bound algorithm and a lower-bounding structure. The lower bound consists of two approaches, which enable the algorithm to simultaneously reduce performing unnecessary exploration. In order to test the efficiency of the algorithm, several problem instances with different board groups have been used. The algorithm developed requires a significantly large computation time to optimally solve very large problems. Thus to speak for the efficiency in terms of solving comparable large industry-size problems, we evaluate the deviation of the algorithm from the lower bound which turns out to be very small, with an average of only 6%, in all of the problem instances considered.     

具有最大作业延迟的生产调度优化算法及仿真

成组作业优化调度问题中的作业根据其加工特点要求可分成若干作业类。同一类的作业连续加工，其后的作业不需要机器设置花费，而不同类的作业连续加工，其后的作业需要机器设置花费。当优化目标是最大作业延迟时，单机成组作业优化调度是HP—hard。本文在利用优化性质的基础上，提出了一种适于大规模优化调度问题的多项式时间算法。仿真实验表明该算法具有良好的性能。     

The total completion time open shop scheduling problem with a given sequence of jobs on one machine

This paper addresses the open shop scheduling problem to minimize the total completion time, provided that one of the machines has to process the jobs in a given sequence. The problem is NP-hard in the strong sense even for the two-machine case. A lower bound is derived based on the optimal solution of a relaxed problem in which the operations on every machine may overlap except for the machine with a given sequence of jobs. This relaxed problem is NP-hard in the ordinary sense, however it can be quickly solved via a decomposition into subset-sum problems. Both heuristic and branch-and-bound algorithm are proposed. Experimental results show that the heuristic is efficient for solving large-scaled problems, and the branch-and-bound algorithm performs well on small-scaled problems.Scope and purposeShop scheduling problems, widely used in the modeling of industrial production processes, are receiving an increasing amount of attention from researchers. To model practical production processes more closely, additional processing restrictions can be introduced, e.g., the resource constraints, the no-wait in process requirement, the precedence constraints, etc. This paper considers the total completion time open shop scheduling problem with a given sequence of jobs on one machine. This model belongs to a new class of shop scheduling problems under machine-dependent precedence constraints. This problem is NP-hard in the strong sense. A heuristic is proposed to efficiently solve large-scaled problems and a branch-and-bound algorithm is presented to optimally solve small-scaled problems. Computational experience is also reported.     

航班过站地面服务的优化调度算法

航班过站服务流程是定位型和零工型的混合流程，其调度问题是一个有时间窗和作业调整时间的多目标多设备并行作业动态排序问题．在分析其区别于一般制造业生产作业排序特点的基础上，给出一个考虑了不同设备加工能力的新的启发式算法——设备能力差分配法．通过对服务作业分类，将多目标优化问题转化为服务类作业排序最优化问题．算例分析显示，能力差分配算法在减少航班延误数量、时间上以及平衡设备生产能力上均优于现有的先到先服务和最小负荷调度算法．     

Deteriorating job scheduling to minimize the number of late jobs with setup times

Deteriorating jobs scheduling problems have been widely studied recently. However, research on scheduling problems with deteriorating jobs has rarely considered explicit setup times. With the current emphasis on customer service and meeting the promised delivery dates, we consider a single-machine scheduling problem to minimize the number of late jobs with deteriorating jobs and setup times in this paper. We derive some dominance properties, a lower bound, and an initial upper bound by using a heuristic algorithm to speed up the search process of the branch-and-bound algorithm. Computational experiments show that the algorithm can solve instances up to 1000 jobs in a reasonable amount of time.     

考虑柔性机器检修的钢管热轧批量调度方法

本文从无缝钢管生产管理中提取并定义了周期性机器柔性检修环境下的钢管热轧批量调度问题,针对无缝钢管热轧阶段的生产特点,将其抽象为一类考虑序列相关设置成本和机器柔性检修的单机调度问题,建立了以最小化机器闲置时间和机器调整时间为优化目标的数学模型。分析闲置时间和检修时点的关系,证明了闲置时间最小化性质,结合问题特征设计了两阶段启发式算法。算法第一阶段采用最小轧机调整时间规则获取具有最小机器调整时间的初始批量轧制序列,第二阶段对初始轧制序列进行全局寻优搜索。基于实际生产数据设计了多种问题规模的对比实验,实验结果表明模型和算法对求解该类问题具有较好效果。     

Single-machine scheduling with deteriorating jobs and setup times to minimize the maximum tardiness

In many realistic production situations, a job processed later consumes more time than the same job when it is processed earlier. Production scheduling in such an environment is known as scheduling with deteriorating jobs. However, research on scheduling problems with deteriorating jobs has rarely considered explicit (separable) setup time (cost). In this paper, we consider a single-machine scheduling problem with deteriorating jobs and setup times to minimize the maximum tardiness. We provide a branch-and-bound algorithm to solve this problem. Computational experiments show that the algorithm can solve instances up to 1000 jobs in reasonable time.     

A robust hybrid approach based on particle swarm optimization and genetic algorithm to minimize the total machine load on unrelated parallel machines

This paper dealt with an unrelated parallel machines scheduling problem with past-sequence-dependent setup times, release dates, deteriorating jobs and learning effects, in which the actual processing time of a job on each machine is given as a function of its starting time, release time and position on the corresponding machine. In addition, the setup time of a job on each machine is proportional to the actual processing times of the already processed jobs on the corresponding machine, i.e., the setup times are past-sequence-dependent (p-s-d). The objective is to determine jointly the jobs assigned to each machine and the order of jobs such that the total machine load is minimized. Since the problem is NP-hard, optimal solution for the instances of realistic size cannot be obtained within a reasonable amount of computational time using exact solution approaches. Hence, an efficient method based on the hybrid particle swarm optimization (PSO) and genetic algorithm (GA), denoted by HPSOGA, is proposed to solve the given problem. In view of the fact that efficiency of the meta-heuristic algorithms is significantly depends on the appropriate design of parameters, the Taguchi method is employed to calibrate and select the optimal levels of parameters. The performance of the proposed method is appraised by comparing its results with GA and PSO with and without local search through computational experiments. The computational results for small sized problems show that the mentioned algorithms are fully effective and viable to generate optimal/near optimal solutions, but when the size of the problem is increased, the HPSOGA obtains better results in comparison with other algorithms.     

电梯群控系统的最优调度仿真

在电梯群控节能优化问题的研究中,电梯群控调度是一个开放、动态、复杂系统的多目标优化问题。但是目前大多数群控系统都采用了乘客最少候梯时间的原则来派梯,并没有从电梯的能源消耗等综合因素来调度电梯,从而降低了电梯群控系统的调度性能。并且传统的调度方法在全局收敛性上不能得到很好的满足。为此提出一种蚁群算法的电梯群控系统来进行最佳电梯调度,利用乘客的候梯时间、电梯耗能和电梯拥挤度作为算法的变量数据,并且建立多目标评价函数的蚁群优化模型的控制器,通过蚁群算法进行仿真,验证了蚁群算法对电梯群控得到良好效果,并解决了电梯群控制器对电梯调度单一和全局快速收敛性的问题,为提高电梯群控调度性能提供了参考。     

Bi-criteria flexible job-shop scheduling with sequence-dependent setup times—Variable neighborhood search approach

In scheduling problems, taking the sequence-dependent setup times into account is one of the important issues that have recently been considered by researchers in the production scheduling field. In this paper, we consider flexible job-shop scheduling problem (FJSP) with sequence-dependent setup times to minimize makespan and mean tardiness. The FJSP consists of two sub-problems from which the first one is to assign each operation to a machine out of a set of capable machines, and the second one deals with sequencing the assigned operations on all machines. To solve this problem, a variable neighborhood search (VNS) algorithm based on integrated approach is proposed. In the presented optimization method, the external loop controlled the stop condition of algorithm and the internal loop executed the search process. To search the solution space, the internal loop used two main search engines, i.e. shake and local search procedures. In addition, neighborhood structures related to the sequencing problem and the assignment problem were employed to generate neighboring solutions. To evaluate the performance of the proposed algorithm, 20 test problems in different sizes are randomly generated. Consequently, computational results and comparisons validate the quality of the proposed approach.     

Single machine scheduling with past-sequence-dependent setup times and learning effects

This paper studies a single machine scheduling problem with setup times and learning considerations. The setup times are proportional to the length of the already scheduled jobs. That is, the setup times are past-sequence-dependent. It is assumed that the learning process reflects a decrease in the process time as a function of the number of repetitions, i.e., as a function of the job position in the sequence. The following objectives are considered: the makespan, the total completion time, the total absolute differences in completion times and the sum of earliness, tardiness and common due-date penalty. Polynomial time algorithms are proposed to optimally solve the above objective functions.     

混合EDA求解三阶段异构并行机装配集成调度问题

本文提出一种混合分布估计算法（hybrid estimation of distribution algorithm，HEDA）用于求解带载重约束的三阶段异构并行机集成调度问题（three-stage heterogeneous parallel machine integrated scheduling problem with capacitated constraint，THPMISP_CC），第一阶段为加工阶段，即带释放时间的多工序异构并行机调度问题；第二阶段为带载重约束的运输阶段，即多维背包优化调度问题；第三阶段为装配阶段.本文研究工件从加工、运输到装配三阶段的集成调度优化问题.首先，本文构建了THPMISP_CC的数学模型，其优化目标为三阶段整体最大完工时间（Makespan）；然后，提出的HEDA用于优化THPMISP_CC；最后，对算法运用于THPMISP_CC模型的结果进行分析和比较，验证模型的可行性及算法的有效性.     

超启发式遗传算法求解模糊柔性作业车间调度

本文提出一种混合超启发式遗传算法(HHGA),用于求解一类采用三角模糊数表示工件加工时间的模糊柔性作业车间调度问题(FFJSP),优化目标为最小化最大模糊完工时间(即makespan).首先,详细分析现有三角模糊数排序准则性质,并充分考虑取大操作的近似误差和模糊度,设计一种更为准确的三角模糊数排序准则,可合理计算FFJSP和其他各类调度问题解的目标函数值.其次,为实现对FFJSP解空间不同区域的有效搜索,HHGA将求解过程分为两层,高层利用带自适应变异算子的遗传算法对6种特定操作(即6种有效邻域操作)的排列进行优化;低层将高层所得的每种排列作为一种启发式算法,用于对低层相应个体进行操作来执行紧凑的变邻域局部搜索并生成新个体,同时加入模拟退火机制来避免搜索陷入局部极小.最后,仿真实验和算法比较验证了所提排序准则和HHGA的有效性.     

时间约束混合流水车间调度问题综述

车间调度是智能制造领域中的核心问题之一, 在经典流水车间调度中, 所有工件按照相同的加工顺序在指 定机床上加工. 混合流水车间调度(HFS)作为流水车间调度的特例, 相比前者增加了机床选择的灵活性, 可以显著 优化系统目标, 但同时也增加了问题求解的难度. 由于时间约束HFS相比基本HFS问题更贴近实际生产过程, 近年 来, 综合考虑各类时间相关约束的HFS问题得到了深入研究. 因此, 本文围绕基本HFS、有限等待时间HFS、带准备 时间HFS、模糊/随机加工时间HFS、多时间约束HFS、时间约束相关多目标HFS等问题开展研究. 针对每一类时间 约束HFS问题, 按照问题规模对当前研究成果进行分类描述, 按照确定性算法、启发式方法、元启发式方法、算法混 合对相关成果进行算法分类, 按照实际工业应用对文献进行归类分析. 另一方面, 围绕交货期、能耗、成本等3类性 能指标, 分析了在各类时间约束HFS问题中的多目标优化相关成果. 最后详细分析了带时间约束HFS问题在问题层 面、算法层面和应用层面存在的挑战性问题和未来研究的方向.     

A double genetic algorithm for the MRCPSP/max

This paper presents a heuristic solution procedure for a very general resource-constrained project scheduling problem. Here, multiple execution modes are available for the individual activities of the project. In addition, minimum as well as maximum time lags between different activities may be given. The objective is to determine a mode and a start time for each activity such that the temporal and resource constraints are met and the project duration is minimised. Project scheduling problems of this type occur e.g. in process industries. The heuristic is a two-phased genetic algorithm with different representation, fitness, crossover operator, etc., in each of them. One of the contributions of the paper is the optimisation in the first phase of a problem dual to the original, the searching for the best modes of the activities. Computational results show that the algorithm outperforms the state-of-the-art algorithms in medium and large instances.     

Single machine batch scheduling problem with fuzzy batch size

In a batch scheduling problem, jobs are grouped (group is called batch) and scheduled in batches, and a setup time is incurred when starting a new batch. Processing times are assumed to be identical for all jobs. Setup times are assumed to be identical for all batches. Though all batch sizes cannot exceed a common upper bound, the upper bound is flexible and satisfaction degree with respect to the upper limit to be maximized is given. Also the other two objectives, i.e., the maximum completion time and the flow-time are to be minimized. Usually there exists no solution optimizing three objectives at a time. Therefore we define non-dominated solutions consisting of batch size, batch number and allocation of jobs to batches. First we propose an efficient algorithm for a sub-problem with fixed upper limit of batch size, fixed batch number based on a Lagrange relaxation procedure. Based on the properties of non-dominated solutions clarified in this paper, we propose an efficient algorithm to find some non-dominated solutions. Finally we summarize the results in this paper and discuss further research problems.     

A two-stage Ant Colony Optimization algorithm to minimize the makespan on unrelated parallel machines with sequence-dependent setup times

This paper addresses the non-preemptive unrelated parallel machine scheduling problem with machine-dependent and sequence-dependent setup times. All jobs are available at time zero, all times are deterministic, and the objective is to minimize the makespan. An Ant Colony Optimization (ACO) algorithm is introduced in this paper and is applied to this NP-hard problem; in particular, the proposed ACO tackles a special structure of the problem, where the ratio of the number of jobs to the number of machines is large (i.e., for a highly utilized set of machines). Its performance is evaluated by comparing its solutions to solutions obtained using Tabu Search and other existing heuristics for the same problem, namely the Partitioning Heuristic and Meta-RaPS. The results show that ACO outperformed the other algorithms.     

Minimizing total weighted flowtime subject to minimum makespan on two identical parallel machines

We study the problem of scheduling n jobs on two identical parallel processors or machines where an optimal schedule is defined as one with the shortest total weighted flowtime (i.e., the sum of the weighted completion time of all jobs), among the set of schedules with minimum makespan (i.e., the completion time of the last job finished). We present a two phase non-linear Integer Programming formulation for its solution, admittedly not to be practical or useful in most cases, but theoretically interesting since it models the problem. Thus, as an alternative, we propose an optimization algorithm, for small problems, and a heuristic, for large problems, to find optimal or near optimal solutions. Furthermore, we perform a computational study to evaluate and compare the effectiveness of the two proposed methods.